Magnetic moment of iron in metallic environments G. W. Fernando Department of Physics, U-46, University of Connecticut, Storrs, Connecticut 06269; Department of Physics, Brookhaven National Laboratory, Upton, New York 11973; and Institute of Fundamental Studies, Hantana Road, Kandy, Sri Lanka R. E. Watson and M. Weinert Department of Physics, Brookhaven National Laboratory, Upton, New York 11973 A. N. Kocharian Department of Physics, California State University, Northridge, California 91330 A. Ratnaweera and K. Tennakone Institute of Fundamental Studies, Hantana Road, Kandy, Sri Lanka Received 28 April 1999 Rare-earth iron nitrides are emerging as an important class of magnetic materials. In certain rare-earth iron compounds, the insertion of small atoms such as nitrogen and boron has resulted in significant changes in the magnetic properties in the form of higher Curie temperatures, enhanced magnetic moments, and stronger anisotropies. In an attempt to understand some of the above, we have focused on two nitride phases of Fe, namely Fe 4 N cubic and Fe 16 N 2 tetragonal. For the Fe 16 N 2 phase, the average Fe moment reported by different experimental groups varies over a wide range of values, from 2.3 B to 3.5 B . We will discuss some of the recent experiments and examine some related theoretical questions with regard to Fe having such an unusually large moment in a metallic environment. Employing a Hubbard-Stoner-like model in addition to local-density results, it is shown that an unusually large on-site Coulomb repulsion is necessary if one is to obtain a moment as large as 3.5 B . I. INTRODUCTION Although a physical picture of quantum magnetism was developed many decades ago, there are still numerous open questions and unresolved problems with regard to under- standing the microscopic mechanisms of ferromagnetism and strong ferromagnetic saturation. Two different theoretical ap- proaches that have been introduced to examine these con- cepts are i band theory based on an effective single-particle picture, where the exchange-correlation splitting is intro- duced through a spin-dependent one-particle potential, as is commonly done within the local-spin-density approximation LSDA based on density-functional theory DFT and ii explicit inclusion of many-body effects through a ‘‘minimal lattice’’ Hamiltonian with a few adjustable parameters such as the Hubbard model to understand the origin of ferromag- netism related to correlated electrons. Although the Hubbard model is usually associated with antiferromagnetism, it is possible to find conditions for ferromagnetic saturation in the metallic state. In contrast, DFT based approaches, at least in principle, are parameter free and the LSDA is well suited for describing itinerant magnetism. The iron nitrides that are discussed in this paper were discovered 1 more than forty years ago. In 1972, Fe 16 N 2 thin films produced by evaporating iron in nitrogen were found to have unusually large saturation polarizations. 2 Although these films did contain substantial amounts of  -Fe, high polarizations were attributed to the presence of the nitride phase. Recent experiments 3–10 related to measuring magnetic moments of iron in iron nitrides have raised various ques- tions, both experimental and theoretical. Early evidence for unusually large moments associated with   -Fe 16 N 2 came from Mo ¨ ssbauer studies of thin films and small particles. 11 A recent NMR study 9 also tends to support the existence of a large site moment of about 3.5 B ) and an average value of  ¯ Fe =2.9 B for the unit cell. However, there is a dissenting point of view, 10,11 that suggests the possibility of an ‘‘egre- gious error’’ in the interpretation of data. Reference 10 points to the presence of a disordered Fe 16 N 2 phase (  ' -N martensite in most of the samples studied. In this paper we will examine some theoretical questions related to magnetism in metallic systems. This will be done through examining first principles as well as parametrized many-body approaches. One such question is whether band theory is capable of yielding such large moments for Fe in a metallic system. This should be addressed from several dif- ferent aspects: first, whether the spin exchange and correla- tion effects included in a LSDA-type approach and possible orbital contributions not included in LSDA can yield such large magnetic moments and second, whether any mean-field theory can describe such situations or whether fluctuations are important. These are somewhat related questions, usually overlooked in most studies. We will argue that within a pa- rametrized mean-field theory it is possible to obtain such large moments—though using somewhat unphysical parameters—while within the usual LSDA it is not possible. This is essentially indicating at least that the spin exchange- correlation effects should be different, or treated more ex- PHYSICAL REVIEW B 1 JANUARY 2000-I VOLUME 61, NUMBER 1 PRB 61 0163-1829/2000/611/3757/$15.00 375 ©2000 The American Physical Society